A131552 Least positive power of 3 having exactly n consecutive 1's in its decimal representation.

4, 19, 93, 334, 841, 3404, 7271, 7720, 44152, 406774, 993948, 2421339, 8786439, 11387707, 93548200

Offset: 1

Author

Shyam Sunder Gupta, Aug 26 2007

Keywords

• more
• nonn
• base

Comments

No more terms < 10^8. - Bert Dobbelaere, Mar 20 2019

Examples

			a(3)=93 because 3^93 (i.e., 235655016338368235499067731945871638181119123) is the smallest power of 3 to contain a run of 3 consecutive ones in its decimal form.
		

Crossrefs

Cf. A195269, A131551, A131550, A131549, A131548, A131547, A131546, A131545, A131544.

Programs

Mathematica

a = ""; Do[ a = StringJoin[a, "1"]; b = StringJoin[a, "1"]; k = 1; While[ StringPosition[ ToString[3^k], a] == {} || StringPosition[ ToString[3^k], b] != {}, k++ ]; Print[k], {n, 1, 10} ]

Python

def A131552(n):
    m, s = 1, '1'*n
    for i in range(1, 10**9):
        m *= 3
        if s in str(m):
            return i
    return "search limit reached." # Chai Wah Wu, Dec 11 2014

Extensions

a(11)-a(14) from Lars Blomberg, Feb 02 2013

Definition edited by Chai Wah Wu, Dec 11 2014

a(15) from Bert Dobbelaere, Mar 20 2019